The topology relation of low voltage distribution network is the basis of power grid state estimation. In view of the topology identification problems in low voltage distribution network, this paper analyzes the feasibility of household variation relation and phase identification by voltage similarity. On this basis, the Hausdorff distance algorithm is applied to construct household variation relation and phase identification process based on the node voltage similarity assessment. The basic criterion is designed based on Hausdorff distance recognition, including the construction of sliding window and the selection of effective voltage data collection optimization method. Finally, the effectiveness of the proposed method is verified by a practical case.